Supersymmetry of the Chiral de Rham Complex

Abstract

We present a superfield formulation of the chiral de Rham complex (CDR) of Malikov-Schechtman-Vaintrob in the setting of a general smooth manifold, and use it to endow CDR with superconformal structures of geometric origin. Given a Riemannian metric, we construct an N=1 structure on CDR (action of the N=1 super--Virasoro, or Neveu--Schwarz, algebra). If the metric is K"ahler, and the manifold Ricci-flat, this is augmented to an N=2 structure. Finally, if the manifold is hyperk"ahler, we obtain an N=4 structure. The superconformal structures are constructed directly from the Levi-Civita connection. These structures provide an analog for CDR of the extended supersymmetries of nonlinear sigma-models.

References added

References in corpus (4)

• Chiral de Rham complex and the half-twisted sigma-model
• Two-Dimensional Models With (0,2) Supersymmetry: Perturbative Aspects
• Supersymmetric vertex algebras
• Chiral Equivariant Cohomology II

Cited by in corpus (30)

• A Worldsheet Theory for Supergravity
• Supersymmetric vertex algebras
• Instantons beyond topological theory II
• Topological twists of supersymmetric algebras of observables
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Generalized Calabi-Yau manifolds and the chiral de Rham complex
• Chiral de Rham complex on Riemannian manifolds and special holonomy
• Mathieu Moonshine and the Geometry of K3 Surfaces
• Supersymmetry of the chiral de Rham complex II: Commuting Sectors
• Twisted chiral de Rham complex, generalized geometry, and T-duality
• Lambda: A Mathematica-package for operator product expansions in vertex algebras
• Snapshots of Conformal Field Theory
• Hodge-elliptic genera and how they govern K3 theories
• Kazama-Suzuki coset construction and its inverse
• The global sections of chiral de Rham complexes on compact Ricci-flat Kähler manifolds II
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• Not Doomed to Fail
• $N=1$ super Virasoro tensor categories
• The global sections of chiral de Rham complexes on compact Ricci-flat Kähler manifolds
• The global sections of the chiral de Rham complex on a Kummer surface
• Supersymmetry and the formal loop space
• Chiral differential operators on supermanifolds
• The Global Sections of Chiral de Rham Complexes on Closed Complex Curves
• $N=2$ and $N=4$ Subalgebras of Super Vertex Operator Algebras
• Strongly Homotopy Chiral Algebroids
• Vertex Algebras and the Equivariant Lie Algebroid Cohomology
• Non-linear sigma models via the chiral de Rham complex
• ${\mathrm{G}}_2$ holonomy manifolds are superconformal